Atmospheric storage tank design

Why it matters

Tank farms hold the raw materials, intermediates and products of every refinery and chemical plant, often tens of thousands of cubic metres each. An atmospheric tank is designed not for internal gas pressure but for the weight of the liquid it holds, so its wall thickness changes from bottom to top. Tank failures — shell ruptures, roof fires, overfills and vacuum collapse during emptying — are among the costliest accidents in the process industries.

Key ideas

What "atmospheric" means. The vapour space is at or very close to atmospheric pressure, kept there by vents. Standards such as API 650 allow small internal pressures (up to roughly 18 kPa gauge in an annex) and IS 803 covers vertical mild-steel oil storage tanks in India; low-pressure tanks above that range follow API 620, and higher pressures need a pressure-vessel code.

Hydrostatic load governs the shell. At depth h the liquid exerts p = ρ·g·h, so the hoop stress — and therefore the required thickness — rises linearly from top to bottom. Tanks are built from horizontal rings of plate called courses, each typically 1.5–2.5 m high; the bottom course is thickest and upper courses step down to a minimum thickness set by the standard for handling and rigidity (it depends on tank diameter; take it from the standard).

One-foot method (API 650). The thickness of each course is calculated at a point 0.3 m (one foot) above the bottom of that course, because the stiffer course below (and the bottom plate for the first course) restrains the lower edge. Two cases are checked: the design condition with the product's specific gravity G, its allowable stress and corrosion allowance, and the hydrostatic-test condition with water (G = 1), a higher test allowable stress and no corrosion allowance. The larger governs. The method applies up to about 60 m diameter; larger tanks use the variable-design-point method.

Bottom and roof. The bottom rests on a prepared foundation, so it carries little stress; a minimum plate thickness plus corrosion allowance is used, often with a thicker annular ring under the shell. Roofs may be:

• Fixed roofs: cone (self-supported or on rafters and columns) or dome. Cheap, but the vapour space breathes as temperature changes, causing evaporation losses. A weak (frangible) roof-to-shell joint is often specified so that an internal explosion tears the roof off rather than splitting the shell.
• Floating roofs (external, or internal under a fixed roof): the roof floats on the liquid with a rim seal, removing most of the vapour space. Used for volatile products such as crude oil, gasoline and naphtha to cut emissions and fire risk.

Venting. Tanks breathe out when filled or heated and in when emptied or cooled. Pressure–vacuum (conservation) vents, open vents with flame arresters, and emergency vents for fire exposure prevent overpressure and vacuum collapse — a tank shell that is only a few millimetres thick cannot resist even a small vacuum.

Other design checks. Wind (shell buckling of the empty tank; wind girders at the top of open-top and floating-roof tanks), seismic sloshing and overturning, foundation settlement, nozzles in the bottom course, and fire protection and bunding (secondary containment). Capacity is described as nominal (geometric), working (between low and high liquid levels) and the overfill margin above the high level.

Proportions. Because the shell gets thicker with height and the soil must carry the full liquid load, large tanks are usually wider than they are tall; the height is commonly limited to about 15–20 m, and the diameter set by the volume required.

Formulas

p = ρ·g·h

• p = hydrostatic pressure (Pa); ρ = liquid density (kg/m³); g = 9.81 m/s²; h = depth below the liquid surface (m).

t = ρ·g·h·D / (2·S·J) (basic hoop-stress thickness at depth h; with D in m, S in Pa, t comes out in m)

t_d = 4.9·D·(H − 0.3)·G / S_d + CA (API 650 one-foot method, design condition) t_t = 4.9·D·(H − 0.3) / S_t (API 650 one-foot method, hydrotest with water)

• t_d, t_t = required course thickness (mm); D = nominal tank diameter (m); H = design liquid level measured from the bottom of the course considered (m); G = design specific gravity of the stored liquid (–); S_d, S_t = allowable stress for design and test conditions (MPa, from the standard); CA = corrosion allowance (mm). The constant 4.9 = 9.81 × 1000 / 2 with unit conversions; joint efficiency is built into the allowable stresses.

V = (π/4)·D²·H (geometric shell volume)

Worked examples

Example 1 (standard): basic hydrostatic thickness Given: tank D = 10 m, maximum liquid height 9 m, liquid density 1100 kg/m³, allowable stress S = 140 MPa, J = 0.85, CA = 1.5 mm.

1. Pressure at the bottom: p = 1100 × 9.81 × 9 = 97 120 Pa = 97.1 kPa.
2. Thickness: t = p·D / (2·S·J) = 97 120 × 10 / (2 × 140 × 10⁶ × 0.85) = 4.08 × 10⁻³ m = 4.08 mm.
3. Add CA: 4.08 + 1.5 = 5.58 mm → 6 mm bottom course (also checking it is not below the standard's minimum).
4. At half depth (4.5 m) the pressure thickness halves to 2.04 mm, so the upper courses are set by the minimum thickness.
5. Capacity: V = π/4 × 10² × 9 = 707 m³.

Example 2 (GATE level): course thicknesses by the one-foot method Given: D = 20 m; design liquid level 12 m; G = 0.85; S_d = 160 MPa; S_t = 171 MPa; CA = 1.5 mm; courses 1.5 m high; plates in even millimetres; minimum shell thickness for this diameter 6 mm (stress values and minimum given; take them from the standard in practice).

1. Course 1 (H = 12 m): t_d = 4.9 × 20 × 11.7 × 0.85 / 160 + 1.5 = 6.09 + 1.5 = 7.59 mm; t_t = 4.9 × 20 × 11.7 / 171 = 6.71 mm → design governs → 8 mm.
2. Course 2 (H = 10.5 m): t_d = 4.9 × 20 × 10.2 × 0.85 / 160 + 1.5 = 6.81 mm; t_t = 5.85 mm → 8 mm.
3. Course 3 (H = 9 m): t_d = 6.03 mm; t_t = 4.99 mm → 8 mm (6.03 just exceeds 6).
4. Course 4 (H = 7.5 m): t_d = 5.25 mm → minimum governs → 6 mm, and all higher courses are 6 mm.
5. Total liquid volume at 12 m: V = π/4 × 20² × 12 = 3770 m³.

Common mistakes

• Designing an atmospheric tank with a pressure-vessel formula using 1 atm as the "pressure" — the load is the liquid head, and the gauge vapour pressure is essentially zero.
• Measuring H from the tank bottom for every course instead of from the bottom of the course being designed.
• Forgetting the hydrotest case with water, which governs for light products (low G).
• Adding the corrosion allowance in the hydrotest case.
• Ignoring vacuum: a thin tank can be sucked in when pumped out with a blocked vent.
• Using a fixed-roof tank for highly volatile products, giving large breathing losses and a flammable vapour space.

For GATE CH

Expect numericals on hydrostatic pressure and shell thickness at a given depth, course-by-course thickness, tank volume and capacity, and conceptual questions on fixed versus floating roofs, venting and why the bottom course is thickest. Practise unit handling in t = ρ·g·h·D/(2SJ).

Quick check

1. Why is the bottom course of a tank the thickest?
2. Which roof type would you choose for gasoline storage, and why?
3. Pressure at the bottom of 10 m of water?
4. Why does the hydrotest case often govern for light hydrocarbons?

Answers: 1. Hydrostatic pressure, and so hoop stress, is greatest at the bottom. 2. A floating roof, to remove the vapour space and cut evaporation losses and fire risk. 3. 1000 × 9.81 × 10 = 98.1 kPa. 4. Water (G = 1) is denser than the product, which can outweigh the higher test allowable stress and the absence of corrosion allowance.